Angle of a semicircle on a ramp

[stewood]

Homework Statement

The semicylinder of mass m and radius r lies on the rough inclined plane for which ϕ = 10∘ and the coefficient of static friction is μs = 0.3. Determine if the semicylinder slides down the plane, and if not, find the angle of tip θ of its base AB

Homework Equations

f=uN

The Attempt at a Solution

I think this requires some weird trigonemetry... I already calculated that the cylinder does not slide down but I cannot calculate the angle of theta

[/B]

 

[mfb]

but I cannot calculate the angle of theta

What did you try so far?
What do you know about equilibrium positions?

 

[haruspex]

Your drawing of the forces could be a little more accurate. Where will the line of action of the normal force intersect AB?

 

[stewood]

What did you try so far?
What do you know about equilibrium positions?

I've tried a few different triangles, but I can't figure it out. I know nothing about equilibrium positions.

 

[stewood]

Your drawing of the forces could be a little more accurate. Where will the line of action of the normal force intersect AB?

How can I calculate that?

 

[stewood]

Never mind, I figured it out. In case your curious you use the law of sines...